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IK_debug.py
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from sympy import *
from time import time
from mpmath import radians
import tf
'''
Format of test case is [ [[EE position],[EE orientation as quaternions]],[WC location],[joint angles]]
You can generate additional test cases by setting up your kuka project and running `$ roslaunch kuka_arm forward_kinematics.launch`
From here you can adjust the joint angles to find thetas, use the gripper to extract positions and orientation (in quaternion xyzw) and lastly use link 5
to find the position of the wrist center. These newly generated test cases can be added to the test_cases dictionary.
'''
test_cases = {1:[[[2.16135,-1.42635,1.55109],
[0.708611,0.186356,-0.157931,0.661967]],
[1.89451,-1.44302,1.69366],
[-0.65,0.45,-0.36,0.95,0.79,0.49]],
2:[[[-0.56754,0.93663,3.0038],
[0.62073, 0.48318,0.38759,0.480629]],
[-0.638,0.64198,2.9988],
[-0.79,-0.11,-2.33,1.94,1.14,-3.68]],
3:[[[-1.3863,0.02074,0.90986],
[0.01735,-0.2179,0.9025,0.371016]],
[-1.1669,-0.17989,0.85137],
[-2.99,-0.12,0.94,4.06,1.29,-4.12]],
4:[],
5:[]}
def rot_x(r):
ROT_x = Matrix([[ 1, 0, 0],
[ 0, cos(r), -sin(r)],
[ 0, sin(r), cos(r)]]) #Roll
return ROT_x
def rot_y(p):
ROT_y = Matrix([[ cos(p), 0, sin(p)],
[ 0, 1, 0],
[ -sin(p), 0, cos(p)]]) #Pitch
return ROT_y
def rot_z(y):
ROT_z = Matrix([[ cos(y), -sin(y), 0],
[ sin(y), cos(y), 0],
[ 0, 0, 1]]) #Yaw
return ROT_z
def trans_matrix(alpha, a, d, q):
T = Matrix([[ cos(q), -sin(q), 0, a],
[ sin(q)*cos(alpha), cos(q)*cos(alpha), -sin(alpha), -sin(alpha)*d],
[ sin(q)*sin(alpha), cos(q)*sin(alpha), cos(alpha), cos(alpha)*d],
[ 0, 0, 0, 1]])
return T
def rad(deg):
# Convert degree to radian.
return deg * pi/180.
def deg(rad):
# Convert radian to degree.
return rad * 180 / pi
def TF_Matrix(alpha, a, d, q):
# Modified DH Transformation Matrix
TF = Matrix([[ cos(q), -sin(q), 0, a],
[sin(q)*cos(alpha), cos(q)*cos(alpha), -sin(alpha), -sin(alpha)*d],
[sin(q)*sin(alpha), cos(q)*sin(alpha), cos(alpha), cos(alpha)*d],
[ 0, 0, 0, 1]])
return TF
def test_code(test_case):
## Set up code
## Do not modify!
x = 0
class Position:
def __init__(self,EE_pos):
self.x = EE_pos[0]
self.y = EE_pos[1]
self.z = EE_pos[2]
class Orientation:
def __init__(self,EE_ori):
self.x = EE_ori[0]
self.y = EE_ori[1]
self.z = EE_ori[2]
self.w = EE_ori[3]
position = Position(test_case[0][0])
orientation = Orientation(test_case[0][1])
class Combine:
def __init__(self,position,orientation):
self.position = position
self.orientation = orientation
comb = Combine(position,orientation)
class Pose:
def __init__(self,comb):
self.poses = [comb]
req = Pose(comb)
start_time = time()
########################################################################################
##
## Insert IK code here!
# Define DH param symbols
d1, d2, d3, d4, d5, d6, d7 = symbols('d1:8') #link offset
a0, a1, a2, a3, a4, a5, a6 = symbols('a0:7') #link length
alpha0, alpha1, alpha2, alpha3, alpha4, alpha5, alpha6 = symbols('alpha0:7') # twist angle
# Joint Angle Symbols
q1, q2, q3, q4, q5, q6, q7 = symbols('q1:8')
# Modified DH parameters
DH_Table = {alpha0: 0, a0: 0, d1: 0.75, q1: q1,
alpha1: rad(-90), a1: 0.35, d2: 0, q2: -rad(90) + q2,
alpha2: 0, a2: 1.25, d3: 0, q3: q3,
alpha3: rad(-90), a3: -0.054, d4: 1.50, q4: q4,
alpha4: rad(90), a4: 0, d5: 0, q5: q5,
alpha5: rad(-90), a5: 0, d6: 0, q6: q6,
alpha6: 0, a6: 0, d7: 0.303, q7: 0}
# Create individual transformation matrices
T0_1 = TF_Matrix(alpha0, a0, d1, q1).subs(DH_Table)
T1_2 = TF_Matrix(alpha1, a1, d2, q2).subs(DH_Table)
T2_3 = TF_Matrix(alpha2, a2, d3, q3).subs(DH_Table)
T3_4 = TF_Matrix(alpha3, a3, d4, q4).subs(DH_Table)
T4_5 = TF_Matrix(alpha4, a4, d5, q5).subs(DH_Table)
T5_6 = TF_Matrix(alpha5, a5, d6, q6).subs(DH_Table)
T6_EE = TF_Matrix(alpha6, a6, d7, q7).subs(DH_Table)
T0_EE = simplify(T0_1 * T1_2 * T2_3 * T3_4 * T4_5 * T5_6 * T6_EE)
print("\nTime taken to create transformation matrices: %04.4f seconds" % (time() - start_time))
# ----- IK Code -------
# Extract end-effector position and orientation from request
# px,py,pz = end-effector position
# roll, pitch, yaw = end-effector orientation
px = req.poses[x].position.x
py = req.poses[x].position.y
pz = req.poses[x].position.z
(roll, pitch, yaw) = tf.transformations.euler_from_quaternion(
[req.poses[x].orientation.x, req.poses[x].orientation.y,
req.poses[x].orientation.z, req.poses[x].orientation.w])
# Find EE rotation matrix
# Define RPY rotation matrices
# (Further reading got from walkthrough)
# http://planning.cs.uiuc.edu/node102.html
r, p, y = symbols('r p y')
ROT_x = rot_x(r) #Roll
ROT_y = rot_y(p) #Pitch
ROT_z = rot_z(y) #Yaw
# ROT_EE = ROT_x * ROT_y * ROT_z
ROT_EE = ROT_z * ROT_y * ROT_x
#Calculate Rotation Error
ROT_Error = ROT_z.subs(y, radians(180)) * ROT_y.subs(p, radians(-90))
ROT_EE = ROT_EE * ROT_Error
ROT_EE = ROT_EE.subs({'r' : roll, 'p' : pitch, 'y' : yaw})
EE = Matrix([[px],
[py],
[pz]])
WC = EE - (0.303) * ROT_EE[:,2]
# Calculate Joint Angles using Geometric IK Method
theta1 = atan2(WC[1],WC[0])
# SSS triangle for theta2 and theta3
side_a = 1.501 # Found by using "measure" tool in RViz.
side_b = sqrt(pow((sqrt(WC[0] * WC[0] + WC[1] * WC[1] ) - 0.35), 2) + pow((WC[2] - 0.75), 2))
side_c = 1.25 # Length of joint 1 to 2
angle_a = acos((side_b * side_b + side_c * side_c - side_a * side_a) / (2 * side_b * side_c))
angle_b = acos((side_a * side_a + side_c * side_c - side_b * side_b) / (2 * side_a * side_c))
angle_c = acos((side_a * side_a + side_b * side_b - side_c * side_c) / (2 * side_a * side_b))
theta2 = pi / 2 - angle_a - atan2(WC[2] - 0.75, sqrt(WC[0] * WC[0] + WC[1] * WC[1]) - 0.35)
theta3 = pi / 2 - (angle_b + 0.036) # 0.036 account for sag in link4 of -0.054m
R0_3 = T0_1[0:3,0:3] * T1_2[0:3,0:3] * T2_3[0:3,0:3]
R0_3 = R0_3.evalf(subs={q1: theta1, q2: theta2, q3: theta3})
R3_6 = R0_3.inv("LU") * ROT_EE
# Euler Angles from rotation matrix
theta5 = atan2(sqrt(R3_6[0,2]*R3_6[0,2] + R3_6[2,2]*R3_6[2,2]),R3_6[1,2])
# select best solution based on theta5
if (theta5 > pi) :
theta4 = atan2(-R3_6[2,2], R3_6[0,2])
theta6 = atan2(R3_6[1,1],-R3_6[1,0])
else:
theta4 = atan2(R3_6[2,2], -R3_6[0,2])
theta6 = atan2(-R3_6[1,1],R3_6[1,0])
##
########################################################################################
########################################################################################
## For additional debugging add your forward kinematics here. Use your previously calculated thetas
## as the input and output the position of your end effector as your_ee = [x,y,z]
## (OPTIONAL) YOUR CODE HERE!
FK = T0_EE.evalf(subs={q1: theta1, q2: theta2, q3: theta3, q4: theta4, q5: theta5, q6: theta6})
## End your code input for forward kinematics here!
########################################################################################
## For error analysis please set the following variables of your WC location and EE location in the format of [x,y,z]
your_wc = [WC[0],WC[1],WC[2]] # <--- Load your calculated WC values in this array
your_ee = [FK[0,3],FK[1,3],FK[2,3]] # <--- Load your calculated end effector value from your forward kinematics
########################################################################################
## Error analysis
print ("\nTotal run time to calculate joint angles from pose is %04.4f seconds" % (time()-start_time))
# Find WC error
if not(sum(your_wc)==3):
wc_x_e = abs(your_wc[0]-test_case[1][0])
wc_y_e = abs(your_wc[1]-test_case[1][1])
wc_z_e = abs(your_wc[2]-test_case[1][2])
wc_offset = sqrt(wc_x_e**2 + wc_y_e**2 + wc_z_e**2)
print ("\nWrist error for x position is: %04.8f" % wc_x_e)
print ("Wrist error for y position is: %04.8f" % wc_y_e)
print ("Wrist error for z position is: %04.8f" % wc_z_e)
print ("Overall wrist offset is: %04.8f units" % wc_offset)
# Find theta errors
t_1_e = abs(theta1-test_case[2][0])
t_2_e = abs(theta2-test_case[2][1])
t_3_e = abs(theta3-test_case[2][2])
t_4_e = abs(theta4-test_case[2][3])
t_5_e = abs(theta5-test_case[2][4])
t_6_e = abs(theta6-test_case[2][5])
print ("\nTheta 1 error is: %04.8f" % t_1_e)
print ("Theta 2 error is: %04.8f" % t_2_e)
print ("Theta 3 error is: %04.8f" % t_3_e)
print ("Theta 4 error is: %04.8f" % t_4_e)
print ("Theta 5 error is: %04.8f" % t_5_e)
print ("Theta 6 error is: %04.8f" % t_6_e)
print ("\n**These theta errors may not be a correct representation of your code, due to the fact \
\nthat the arm can have muliple positions. It is best to add your forward kinmeatics to \
\nconfirm whether your code is working or not**")
print (" ")
# Find FK EE error
if not(sum(your_ee)==3):
ee_x_e = abs(your_ee[0]-test_case[0][0][0])
ee_y_e = abs(your_ee[1]-test_case[0][0][1])
ee_z_e = abs(your_ee[2]-test_case[0][0][2])
ee_offset = sqrt(ee_x_e**2 + ee_y_e**2 + ee_z_e**2)
print ("\nEnd effector error for x position is: %04.8f" % ee_x_e)
print ("End effector error for y position is: %04.8f" % ee_y_e)
print ("End effector error for z position is: %04.8f" % ee_z_e)
print ("Overall end effector offset is: %04.8f units \n" % ee_offset)
if __name__ == "__main__":
# Change test case number for different scenarios
test_case_number = 1
test_code(test_cases[test_case_number])